The spectral response of a two-arm optical interferometer is a periodic function having a sinusoidal shape. The period of this function is inversely proportional to the difference in length between the two arms of the interferometer. This difference is called the optical path difference (OPD). Any perturbation on the length of any or both arms, whether by geometrical deformation of the interferometer or by perturbation in the optical path traveled by the light will change the period of the spectral response.
This property of optical interferometers to encode their OPD in the spectrum (or phase) of light is well known in the art and is often used to detect a variety of physical parameters, as shown in U.S. Pat. No. 4,714,342 (Jackson et al.), U.S. Pat. No. 4,360,272 (Schmadel et al.), U.S. Pat. No. 4,942,767 (Haritonidis et al.), U.S. Pat. No. 5,206,924 (Kersey), U.S. Pat. No. 4,688,940 (Sommargren et al.), U.S. Pat. No. 5,179,424 (Lequime et al.), U.S. Pat. No. 5,200,796 (Lequime), U.S. Pat. No. 5,349,439 (Graindorge et al.), U.S. Pat. No. 5,202,939 (Belleville et al.), and in the articles entitled “High accuracy position-sensing with fiber-coupled white-light interferometers”, T. Bosselmann and R. Ulrich Proceedings of OFS 2 (Stuttgart), pp. 361-364 (1984), and “White-light interferometry in optical fiber sensors”, H. C. Lefevre, Proceedings of the 7th Optical Fibre Sensors Conference (OFS 7), 1990.
One common example is the Michelson interferometer used in optical displacement sensor. In its simplest form, it consists of a laser source, a beam splitter, two mirrors and a detector. The light is first divided in two beams of different paths by the beam splitter. Each beam is then reflected back by a mirror along its path toward the beam splitter. The two beams then recombine and the resulting interference is incident on the detector. Since the laser emits a very narrow spectrum, in all practical manner a single frequency of light, the detector will sense an intensity that depends on the OPD of the interferometer. So if one mirror is kept at a fixed distance from the beam splitter (the reference arm), the light intensity measured by the detector will vary in a sinusoidal manner when the other mirror is moving (the measurement arm). Hence, if the intensity undergoes a variation that goes through a maximum, a minimum, and a maximum again, it means that the mirror has moved on a distance that is at least equal to half the wavelength of the light spectrum. Measuring the displacement is then a simple matter of counting pulses.
However, simple and elegant this method might appear, it suffers from several handicaps. First, one cannot tell if the mirror is moving in one direction or the other. Also, alignment variations or intensity variations of the source can severely affect the displacement reading, as these variations can be interpreted as a legitimate pulse.
Some of the problems in this arrangement can be alleviated by finding a way to add a second signal that would behave differently than the first to the movement of the mirror. Ideally, the two signals would share the same periodicity but with a phase offset of 90 degrees. One possibility is to use two orthogonal polarizations in the reference and measurement paths. The recombined light is then split in two beams again. One beam goes through a polarizer before entering the first detector. The other beam goes through a quarter-wave plate and a polarizer before entering the second detector. The two resulting signals are said to be in quadrature: when one signal is at its maximum, the other signal is half-way between its minimum and its maximum. Not only this quadrature system yields a sense of direction, but it also permits a higher degree of fringe interpolation. One can also employ a heterodyne scheme to further enhance this system and obtain more robustness to light source alignment variations. This can be accomplished by using a two-frequency laser and high-frequency phase detection electronics as shown in the aforementioned patent of Sommargren et al.
Although these refinements can lead to a very performing system, they add a lot of complexity and costs. And even with all these refinements, the use of narrow bandwidth laser sources makes this configuration an inherently relative measurement system. It only measures the displacement, i.e. the variation of distance, of the moving mirror. When this apparatus is first turned on, there is no way of telling what is the absolute OPD of the interferometer.
Another approach to the detection of the OPD of an interferometer takes advantage of the limited coherence length of a large spectral width source. The coherence length of light is inversely proportional to the spectral width. A simple implementation of this so-called white-light interferometry technique (see the article entitled “Application de la modulation spectrale à la transmission de l'information” C. Delisle and P. Cielo, Can. J. Phys., p. 1047 (1974), the aforementioned articles of T. Bosselmann et al. and of H. C. Lefevre, and the aforementioned US patent of Lequime) is illustrated in FIG. 1. Light from a broadband light source 2 is incident on a first interferometer 4 whose optical path difference OPD1 is greater than the coherence length of the light. Inside this first interferometer 4 (here represented as a Mach-Zehnder type), the coherence functions from the two arms do not overlap because of the difference between the two arms' length. Hence no interference can be seen at the output of the first interferometer 4. The interference can be recovered by the use of a second interferometer 6 for which the optical path difference OPD2 is close to OPD1 to within the coherence length of the light. This is illustrated in FIG. 1 where the leading lobe of the coherence function in the longest arm interferes with the lagging lobe of the coherence function in the shortest arm.
FIGS. 2A-B represent the intensity of light at the output of the second interferometer 6 (shown in FIG. 1) with respect to the variation of its OPD (i.e. OPD2) for two fixed different values of OPD1. When OPD2 is near zero, one can see an interference 8 which is only due to the fact that OPD2 is shorter than the coherence length. The period of these interference fringes 8 is equal to the central wavelength of the light spectrum. When OPD2 progresses toward higher values, this interference progressively disappears. When the value of OPD2 approaches that of OPD1, another interference pattern 10 appears, with a maximum visibility at the point where OPD2 is equal to OPD1. The period of this second set of interference fringes 10 is the same as the first interference, but the point of maximum visibility always corresponds to the centre of a fringe (whether a minimum or a maximum intensity, depending on the interferometer arrangement).
This arrangement suggests a simple way to devise an optical sensor system where the first interferometer (the sensing interferometer) is acting as a sensitive device against the parameter to be measured, whereas the second is used as a reference (or reading) interferometer. If the reading interferometer is made to vary its OPD in a known fashion, one can simply correlates the centre fringe position to the known OPD value to obtain the exact value of the OPD of the remote sensing interferometer.
Instead of time-scanning the reading interferometer, another scheme has been proposed where the light from the sensing interferometer is spread on the surface of a Fizeau interferometer. A Fizeau interferometer consists of two partially reflecting mirrors at a small angle with respect to each other. It can be seen as a continuous succession of low-finesse Fabry-Pérot interferometers where the cavity length varies as a function of the position along the wedge. An array of photo detectors placed behind the Fizeau interferometer will hence show a pattern similar to that of FIGS. 2A-B, the image of the pattern moving along the wedge as the sensing interferometer OPD varies (see the aforementioned US patents of Graindorge et al. and Belleville et al.).
This arrangement yields an absolute measure of the OPD of the sensing interferometer with a very high resolution. It is also very reliable because the demodulation instrument contains no moving part. However, the measurement speed of this system is limited by the slow response time of the detector array. It is also somewhat noisy because the light is inefficiently spread amongst the many detectors in the detector array.